In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity and singular potential is considered.We prove the local existence of solution by Galerkin method and contraction mapping theorem.Moreov...In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity and singular potential is considered.We prove the local existence of solution by Galerkin method and contraction mapping theorem.Moreover,we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0.Finally,we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0.展开更多
In this paper, an efficient numerical method is proposed to solve the Caputo-Riesz fractional diffusion equation with fractional Robin boundary conditions. We approximate the Riesz space fractional derivatives using t...In this paper, an efficient numerical method is proposed to solve the Caputo-Riesz fractional diffusion equation with fractional Robin boundary conditions. We approximate the Riesz space fractional derivatives using the fractional central difference scheme with second-order accurate. A priori estimation of the solution of the numerical scheme is given, and the stability and convergence of the numerical scheme are analyzed.Finally, a numerical example is used to verify the accuracy and efficiency of the numerical method.展开更多
In this paper, the following ferro magnetic chain equation with periodic initial value problem is considered:The seni-discrete and fully discrete Fourier spectral and pseudo-spectral schemes are proposed. The converge...In this paper, the following ferro magnetic chain equation with periodic initial value problem is considered:The seni-discrete and fully discrete Fourier spectral and pseudo-spectral schemes are proposed. The convergences and stabilities for the schemes are proved. More over, the algorithm for the pseudo-spectral method is provided. Finally, some numerical experiments are given and compared with difference methods.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11271141).
文摘In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity and singular potential is considered.We prove the local existence of solution by Galerkin method and contraction mapping theorem.Moreover,we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0.Finally,we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0.
基金Supported by National Natural Science Foundation of China(Grant No.11271141)。
文摘In this paper, an efficient numerical method is proposed to solve the Caputo-Riesz fractional diffusion equation with fractional Robin boundary conditions. We approximate the Riesz space fractional derivatives using the fractional central difference scheme with second-order accurate. A priori estimation of the solution of the numerical scheme is given, and the stability and convergence of the numerical scheme are analyzed.Finally, a numerical example is used to verify the accuracy and efficiency of the numerical method.
文摘In this paper, the following ferro magnetic chain equation with periodic initial value problem is considered:The seni-discrete and fully discrete Fourier spectral and pseudo-spectral schemes are proposed. The convergences and stabilities for the schemes are proved. More over, the algorithm for the pseudo-spectral method is provided. Finally, some numerical experiments are given and compared with difference methods.
